Wallpaper groups (#23)

Reviewed-on: #23

README.md

@@ -1,7 +1,7 @@
 [tinymist]: https://marketplace.visualstudio.com/items?itemName=myriad-dreamin.tinymist
 [latex-workshop]: https://marketplace.visualstudio.com/items?itemName=James-Yu.latex-workshop
 [CC BY-NC-SA 4.0]: https://creativecommons.org/licenses/by-nc-sa/4.0
-[betalupi.com/handouts]: https://static.betalupi.com/ormc
+[betalupi.com/handouts]: https://betalupi.com/handouts
 [ORMC]: https://circles.math.ucla.edu/circles/
 [Overleaf]: https://overleaf.com
 [Typst.app]: https://typst.app
@@ -26,7 +26,7 @@ By submitting or editing a handout in this repository, you agree to release it u
 
 ## 🛠️ Contributing
 
-If you want to use one of these handouts for a class, see [`betalupi.com/handouts`](https://betalupi.com/handouts). \
+If you want to use one of these handouts for a class, see [betalupi.com/handouts]. \
 You only need to read this section if you want to edit these handouts.
 
 ### Setup
@@ -56,7 +56,7 @@ This repository is organized as follows:
 -   [`./tools`](./tools) contains build scripts, [`./.github`](./.github) configures automation. \
     You can ignore everything in these directories.
 
-All handouts in this repository are based on `ormc_handout.cls` or `handout@0.1.0`.
+All handouts in this repository are based on `handout.cls` or `handout@0.1.0`.
 
 -   If you're using Typst (preferred), read [`docs-typst.md`](./docs-typst.md)
 -   If you're still using LaTeX, read [`docs-latex.md`](./docs-latex.md).
@@ -95,8 +95,8 @@ _(I do not recommend this. The default toolchain makes it easier to share improv
 ### For LaTeX:
 
 1. Get the handout's directory (i.e, download the whole repo as a zip and extract the folder you want.)
-2. Download [`./resources/ormc_handout.cls`](./resources/ormc_handout.cls)
-3. Put this `ormc_handout.cls` in the same directory as the handout.
+2. Download [`./resources/handout.cls`](./resources/handout.cls)
+3. Put this `handout.cls` in the same directory as the handout.
 4. Fix the include path at the top of `main.tex`:
 
 You'll need to replace
@@ -104,7 +104,7 @@ You'll need to replace
 ```latex
 \documentclass[
 	...
-]{../../../lib/tex/ormc_handout}
+]{../../../lib/tex/handout}
 ```
 
 with
@@ -112,11 +112,11 @@ with
 ```latex
 \documentclass[
 	...
-]{ormc_handout}
+]{handout}
 ```
 
 5. Make a new overleaf project with the resulting directory.
-6. **Do not use pdflatex**, it misbehaves with `ormc_handout`. Tell Overleaf to use XeLaTeX.
+6. **Do not use pdflatex**, it misbehaves with `handout`. Tell Overleaf to use XeLaTeX.
 
 ### For Typst:
 
@@ -124,5 +124,5 @@ Out-of-band typst compilation isn't supported. Clone the repository and use vsco
 This is because typst can't import packages from a relative path.
 
 If you _really_ want it, standalone typst compilation _is_ possible. \
-Follow the LaTeX instructions, but fix `handout@0.1.0` instead of `ormc_handout`. \
+Follow the LaTeX instructions, but fix `handout@0.1.0` instead of `handout`. \
 You'll figure it out.

docs-latex.md

@@ -1,23 +1,25 @@
 # LaTeX documentation
 
-All LaTeX handouts are based on [`ormc_handout.cls`](./lib/tex/ormc_handout.cls). \
+All LaTeX handouts are based on [`handout.cls`](./lib/tex/handout.cls). \
 This class is based on `article.cls`, and should work with most LaTeX packages.
 
 The best way to start a new document is to make a copy of an existing one.
-- [Advanced/Cryptography](./src/Advanced/Cryptography) is a good example of a simple handout.
-- [Advanced/DFAs](./src/Advanced/DFAs) is a good example of a handout with graphs.
-- [Advanced/Geometric Optimization](./src/Advanced/Geometric%20Optimization) is a good example of a handout with geometry.
 
+-   [Advanced/Cryptography](./src/Advanced/Cryptography) is a good example of a simple handout.
+-   [Advanced/DFAs](./src/Advanced/DFAs) is a good example of a handout with graphs.
+-   [Advanced/Geometric Optimization](./src/Advanced/Geometric%20Optimization) is a good example of a handout with geometry.
 
 ## Notes
-- Compile your handouts with XeLaTeX. \
-  `pdflatex` is known to misbehave with `ormc_handout.cls`. \
-  This will happen by default if you use vscode. \
-  If you use Overleaf, you'll have to configure it manually (see document settings).
+
+-   Compile your handouts with XeLaTeX. \
+    `pdflatex` is known to misbehave with `handout.cls`. \
+    This will happen by default if you use vscode. \
+    If you use Overleaf, you'll have to configure it manually (see document settings).
 
 ## Document Options
 
 Document options are passed to `\documentclass`, as follows:
+
 ```latex
 \documentclass[
 	% Show solutions is `solutions` is provided,
@@ -37,49 +39,52 @@ Document options are passed to `\documentclass`, as follows:
 	% This should only be used for single-page handouts
 	% (e.g, warm-ups)
 	nopagenumber
-]{ormc_handout}
+]{handout}
 ```
 
 Use `geometry` to change margins and page dimensions. US letter is the default.
 
-
 ## Utilities
-- `\say{text}`: Puts text in quotes, handling details like period spacing. Courtesy of `dirtytalk`.
-- `\note[Type]{text}`: Makes a note.
-- `\hint{text}`: Shorthand for `\note[Hint]{text}`
+
+-   `\say{text}`: Puts text in quotes, handling details like period spacing. Courtesy of `dirtytalk`.
+-   `\note[Type]{text}`: Makes a note.
+-   `\hint{text}`: Shorthand for `\note[Hint]{text}`
 
 ## Sections
 
-The usual LaTeX title-customization techniques *WILL NOT WORK* with this class. \
+The usual LaTeX title-customization techniques _WILL NOT WORK_ with this class. \
 Don't even try to load `titlesec`.
 
-`ormc_handout.cls` supports two levels of sections:
-- `\section`, for large parts of the handout
-- `\definition`, `\theorem`, `\proposition`, `\example`, `\remark`, `\problem`, and `\problempart`
+`handout.cls` supports two levels of sections:
+
+-   `\section`, for large parts of the handout
+-   `\definition`, `\theorem`, `\proposition`, `\example`, `\remark`, `\problem`, and `\problempart`
 
 All these macros have the following syntax: `\problem{title}<label>`
-- `title` is the problem's title, and may be empty.
-- `label` is the problem's label. This is optional. \
-  If a label is provided, this section may be referenced with `\ref{label}`.
+
+-   `title` is the problem's title, and may be empty.
+-   `label` is the problem's label. This is optional. \
+    If a label is provided, this section may be referenced with `\ref{label}`.
 
 Examples:
-- `\problem{}`
-- `\problem{Bonus}`
-- `\problem{}<gcd>`, which may be referenced with `\ref{gcd}`
+
+-   `\problem{}`
+-   `\problem{Bonus}`
+-   `\problem{}<gcd>`, which may be referenced with `\ref{gcd}`
 
 Do **not** use `\begin{problem} ... \end{problem}`. \
 Sections are macros, not environments.
 
 ## Environments:
 
-- `\begin{solution}`: A fancy red for solutions to problems. \
-	This is hidden if the `nosolutions` is provided.
-- `\begin{instrutornote}`: A fancy blue box for instructor notes. \
-	This is hidden if the `nosolutions` is provided.
-- `\begin{examplesolution}`: A fancy gray for sample solutions. \
-	This is never hidden.
+-   `\begin{solution}`: A fancy red for solutions to problems. \
+    This is hidden if the `nosolutions` is provided.
+-   `\begin{instrutornote}`: A fancy blue box for instructor notes. \
+    This is hidden if the `nosolutions` is provided.
+-   `\begin{examplesolution}`: A fancy gray for sample solutions. \
+    This is never hidden.
 
 All the above environments break across pages and may safely be nested.
 
 Each of these environments also provides the `\linehack` macro, which draws a line across the box. \
-This is useful for, say, solutions to multipart problems.
+This is useful for, say, solutions to multipart problems.

docs-typst.md

@@ -4,23 +4,27 @@ See [typst.app/docs](https://typst.app/docs) for typst's documentation. \
 All typst handouts are based on [`handout@0.1.0`](./lib/typst/local/handout/0.1.0).
 
 The best way to start a new document is to make a copy of an existing one.
-- [Advanced/Tropical Polynomials](./src/Advanced/Tropical%20Polynomials) is a good place to start.
-- [Warm-Ups/Painting](./src/Warm-Ups/Painting) is a good example of tikz-like pictures.
 
+-   [Advanced/Tropical Polynomials](./src/Advanced/Tropical%20Polynomials) is a good place to start.
+-   [Warm-Ups/Painting](./src/Warm-Ups/Painting) is a good example of tikz-like pictures.
 
 ## Notes
-- Typst's equivalent of tikz is cetz ([homepage](https://cetz-package.github.io), [docs](https://cetz-package.github.io/docs/api))
-- Typst handouts are always compiled with solutions. \
-  Handouts without solutions are automatically compiled and published at [betalupi.com/handouts](https://static.betalupi.com/ormc). \
-  If you'd like to compile a student handout manually, run the following command in a handout directory:
+
+-   Typst's equivalent of tikz is cetz ([homepage](https://cetz-package.github.io), [docs](https://cetz-package.github.io/docs/api))
+-   Typst handouts are always compiled with solutions. \
+    Handouts without solutions are automatically compiled and published at [betalupi.com/handouts](https://betalupi.com/handouts). \
+    If you'd like to compile a student handout manually, run the following command in a handout directory:
+
 ```bash
 typst compile main.typ --package-path ../../../lib/typst --input show_solutions=false
 ```
+
 Where `package_path` is a relative path to [./lib/typst](./lib/typst).
 
 ## Document Options
 
 All typst handouts start with the following:
+
 ```typst
 #show: handout.with(
   // Should match `meta.toml`
@@ -38,39 +42,44 @@ All typst handouts start with the following:
 ```
 
 ## Notable commands
-- `#v(1fr)`: Like LaTeX's `\vfill`. Creates whitespace that grows automatically. \
-  `fr` means "fraction". `#v(2fr)` will fill twice as much space as `#v(1fr)` on the same page.
+
+-   `#v(1fr)`: Like LaTeX's `\vfill`. Creates whitespace that grows automatically. \
+    `fr` means "fraction". `#v(2fr)` will fill twice as much space as `#v(1fr)` on the same page.
 
 ## Utilities
-- `#note([content], type: "Note type")`: Makes a note. `type` is optional.
-- `#hint([content])`: Shorthand for `#note([content], type: "Hint")`
-- `#solution([content])`: A pretty box for solutions. Hidden in student handouts.
-- `#examplesolution([content])`: Like `#solution()`, but is never hidden.
-- `#if_solutions([content])`: Shows content only if we are showing solutions.
-- `#if_no_solutions([content])`: Shows content only if we **aren't** showing solutions.
+
+-   `#note([content], type: "Note type")`: Makes a note. `type` is optional.
+-   `#hint([content])`: Shorthand for `#note([content], type: "Hint")`
+-   `#solution([content])`: A pretty box for solutions. Hidden in student handouts.
+-   `#examplesolution([content])`: Like `#solution()`, but is never hidden.
+-   `#if_solutions([content])`: Shows content only if we are showing solutions.
+-   `#if_no_solutions([content])`: Shows content only if we **aren't** showing solutions.
 
 ## Sections
+
 High-level sections are denoted with `=`. \
 Subsections start with `==`, subsubsections with `===`, and so on. \
 **`handout@0.1.0` is only designed to use `=`, subsections might be ugly.**
 
-
 `handout@0.1.0` also provides the following commands:
-- `problem`
-- `definition`
-- `theorem`
-- `example`
-- `remark`
+
+-   `problem`
+-   `definition`
+-   `theorem`
+-   `example`
+-   `remark`
 
 These all have the same syntax: `#problem("title", label: "label")`
-- `title` is the problem's title, and may be omitted.
-- `label` is the problem's label. This is optional. \
-  If a label is provided, this problem can be referenced with `@label`
+
+-   `title` is the problem's title, and may be omitted.
+-   `label` is the problem's label. This is optional. \
+    If a label is provided, this problem can be referenced with `@label`
 
 **Examples:**
-- `#problem()`
-- `#problem("Bonus")`
-- `#problem(label: "gcd")`, which may be referenced with `@gcd`
+
+-   `#problem()`
+-   `#problem("Bonus")`
+-   `#problem(label: "gcd")`, which may be referenced with `@gcd`
 
 ### Complete example:
 
@@ -91,4 +100,4 @@ Consider the polynomial $f(x) = x^3 + 1x^2 + 3x + 6$.
 #problem()
 Recall @imaproblem.
 - use this graph to find the roots of $f$
-```
+```

lib/tex/handout.cls

@@ -1,5 +1,5 @@
 \NeedsTeXFormat{LaTeX2e}
-\ProvidesClass{../../../lib/tex/ormc_handout}[2023/05/29 2.0.2 ORMC Handout]
+\ProvidesClass{../../../lib/tex/handout}[2025/03/02 2.0.2 Mark's handout class]
 
 
 
@@ -13,7 +13,7 @@
 \@twocolumnfalse
 \@twosidefalse
 \@mparswitchfalse
-% ORMC-specific
+% Handout-specific
 \newif{\if@solutions} % If false, solutions and instructor notes are hidden.
 \newif{\if@singlenumbering} % If true, the same counter is used for all objects.
 \newif{\if@nopagenumber} % If true, don't number pages.
@@ -25,7 +25,7 @@
 \DeclareOption{10pt}{\renewcommand\@ptsize{0}}
 \DeclareOption{11pt}{\renewcommand\@ptsize{1}}
 \DeclareOption{12pt}{\renewcommand\@ptsize{2}}
-% ORMC-specific options
+% Handout-specific options
 \DeclareOption{solutions}{\@solutionstrue}
 \DeclareOption{nosolutions}{\@solutionsfalse}
 \DeclareOption{multinumbering}{\@singlenumberingfalse}
@@ -37,7 +37,7 @@
 \DeclareOption{showwarning}{\@nowarningfalse}
 \DeclareOption{hidewarning}{\@nowarningtrue}
 \DeclareOption{unfinished}{\@unfinishedtrue}
-\DeclareOption*{\ClassWarning{ormc_handout}{\CurrentOption ignored}}
+\DeclareOption*{\ClassWarning{handout}{\CurrentOption ignored}}
 
 \@unfinishedfalse
 \ExecuteOptions{
@@ -629,12 +629,12 @@
 
 % Keep track of the current background color.
 % Useful for transparent tikz drawings.
-\def\ORMCbgcolor{white}
+\def\bgcolor{white}
 
 % Make a box environment.
 % These can safely be nested.
 % Args: title, back color, frame color.
-\newenvironment{ORMCbox}[3]{
+\newenvironment{hobox}[3]{
 	% \linehack draws a line across a tcolorbox.
 	% tcolorbox only supports two sections, but
 	% this hack allows us to have more.
@@ -653,7 +653,7 @@
 
 	% Keep track of the current background color.
 	% Useful for transparent tikz drawings.
-	\def\ORMCbgcolor{#2}
+	\def\bgcolor{#2}
 
 	\begin{tcolorbox}[
 		enhanced,
@@ -675,21 +675,21 @@
 }
 
 \newenvironment{examplesolution}{
-	\begin{ORMCbox}{Example Solution}{black!10!white}{black!65!white}
+	\begin{hobox}{Example Solution}{black!10!white}{black!65!white}
 } {
-	\end{ORMCbox}
+	\end{hobox}
 }
 
 \if@solutions
 	\newenvironment{solution}{
-		\begin{ORMCbox}{Solution}{ored!10!white}{ored}
+		\begin{hobox}{Solution}{ored!10!white}{ored}
 	} {
-		\end{ORMCbox}
+		\end{hobox}
 	}
 	\newenvironment{instructornote}{
-		\begin{ORMCbox}{Note for Instructors}{ocyan!10!white}{ocyan}
+		\begin{hobox}{Note for Instructors}{ocyan!10!white}{ocyan}
 	} {
-		\end{ORMCbox}
+		\end{hobox}
 	}
 \else
 	\excludecomment{solution}

lib/tex/macros.sty

@@ -1,5 +1,5 @@
 \NeedsTeXFormat{LaTeX2e}
-\ProvidesPackage{../../../lib/tex/macros}[2023/10/16 ORMC Macros]
+\ProvidesPackage{../../../lib/tex/macros}[2025/03/02 Handout macros]
 
 \RequirePackage{hyperref}
 \RequirePackage{pgf}

lib/typst/local/handout/0.1.0/lib.typ

@@ -49,19 +49,28 @@
   // Text style
   set text(font: "New Computer Modern")
   set par(
-    leading: 0.55em,
-    first-line-indent: 0mm,
-    justify: true,
+    leading: 0.5em,
     spacing: 0.5em,
+
+    first-line-indent: 0mm,
+    hanging-indent: 0mm,
+    justify: true,
   )
 
   //
   // List style
-  show list: set block(spacing: 0.5em, below: 1em)
   set list(
-    tight: false,
-    indent: 5mm,
-    spacing: 3mm,
+    indent: 4mm,
+    body-indent: 1.5mm,
+
+    // Manually set spacing,
+    // `tight` has no effect.
+    spacing: 2mm,
+  )
+  set enum(
+    indent: 4mm,
+    body-indent: 1.5mm,
+    spacing: 2mm,
   )
 
   //
@@ -94,7 +103,9 @@
   // Make handout title
   {
     import "header.typ": make_header, solution_warning, short_solution_warning
-    import "solution.typ": show_solutions
+    import "solution.typ": solutions_state, reset_solutions
+
+    reset_solutions()
 
     let url = link(
       "https://betalupi.com/handouts",
@@ -109,12 +120,13 @@
       top_right: url,
     )
 
-
-    if show_solutions {
-      if short_warning {
-        short_solution_warning()
-      } else {
-        solution_warning()
+    context {
+      if solutions_state.get() {
+        if short_warning {
+          short_solution_warning()
+        } else {
+          solution_warning()
+        }
       }
     }
   }

lib/typst/local/handout/0.1.0/solution.typ

@@ -1,34 +1,63 @@
 #import "misc.typ": ored, oblue
 
+
 /// If false, hide instructor info.
-///
-/// Compile with the following command to hide solutions:
-/// `typst compile main.typ --input show_solutions=false`
+/// If true, show it.
 ///
 /// Solutions are shown by default. This behavior
 /// is less surprising than hiding content by default.
-#let show_solutions = {
+#let solutions_state = state("solutions_state", true)
+
+/// Force solutions to be hidden after this point.
+///
+/// This function produces content that must be
+/// included in the document. If it is not included,
+/// this function will have no effect.
+#let hide_solutions() = {
+  return solutions_state.update(x => false)
+}
+
+/// Force solutions to be shown after this point.
+///
+/// This function produces content that must be
+/// included in the document. If it is not included,
+/// this function will have no effect.
+#let show_solutions() = {
+  return solutions_state.update(x => true)
+}
+
+
+
+/// Reset the solution flag to its default value.
+/// This value is determined by compile flags:
+/// Compile with the following command to hide solutions:
+/// `typst compile main.typ --input show_solutions=false`
+///
+/// Solutions are shown by default.
+///
+/// This function produces content that must be
+/// included in the document. If it is not included,
+/// this function will have no effect.
+#let reset_solutions() = {
   if "show_solutions" in sys.inputs {
-    // Show solutions unless they're explicitly disabled
-    not (
+    if (
       sys.inputs.show_solutions == "false" or sys.inputs.show_solutions == "no"
-    )
-  } else {
-    // Show solutions by default
-    true
+    ) {
+      return solutions_state.update(x => false)
+    }
   }
 }
 
-#let if_solutions(content) = {
-  if show_solutions { content }
+#let if_solutions(content) = context {
+  if solutions_state.get() { content }
 }
 
-#let if_no_solutions(content) = {
-  if not show_solutions { content }
+#let if_no_solutions(content) = context {
+  if not solutions_state.get() { content }
 }
 
-#let if_solutions_else(if_yes, if_no) = {
-  if show_solutions { if_yes } else { if_no }
+#let if_solutions_else(if_yes, if_no) = context {
+  if solutions_state.get() { if_yes } else { if_no }
 }
 
 #let solution(content) = {

src/Advanced/Compression/main.tex

@@ -3,7 +3,7 @@
 \documentclass[
 	solutions,
 	singlenumbering
-]{../../../lib/tex/ormc_handout}
+]{../../../lib/tex/handout}
 \usepackage{../../../lib/tex/macros}
 
 \input{tikzset.tex}

src/Advanced/Compression/tikzset.tex

@@ -24,7 +24,7 @@
 	label/.style = {
 		rectangle,
 		% For automatic red background in solutions
-		fill = \ORMCbgcolor,
+		fill = \bgcolor,
 		draw = none,
 		rounded corners = 0mm
 	},
@@ -32,7 +32,7 @@
 	% Nodes
 	edg/.style = {
 		midway,
-		fill = \ORMCbgcolor,
+		fill = \bgcolor,
 		text = gray
 	},
 	int/.style = {},

src/Advanced/Continued Fractions/main.tex

@@ -5,7 +5,7 @@
 	shortwarning,
 	singlenumbering,
 	unfinished
-]{../../../lib/tex/ormc_handout}
+]{../../../lib/tex/handout}
 \usepackage{../../../lib/tex/macros}
 
 \usepackage{multicol}

src/Advanced/Cryptography/main.tex

@@ -4,7 +4,7 @@
 	solutions,
 	singlenumbering,
 	shortwarning
-]{../../../lib/tex/ormc_handout}
+]{../../../lib/tex/handout}
 \usepackage{../../../lib/tex/macros}
 
 \usepackage{multicol}

src/Advanced/DFAs/main.tex

@@ -3,7 +3,7 @@
 \documentclass[
 	solutions,
 	singlenumbering
-]{../../../lib/tex/ormc_handout}
+]{../../../lib/tex/handout}
 \usepackage{../../../lib/tex/macros}
 
 \input{tikzset.tex}

src/Advanced/DFAs/tikzset.tex

@@ -24,7 +24,7 @@
 	label/.style = {
 		rectangle,
 		% For automatic red background in solutions
-		fill = \ORMCbgcolor,
+		fill = \bgcolor,
 		draw = none,
 		rounded corners = 0mm
 	},

src/Advanced/De Bruijn/main.tex

@@ -3,7 +3,7 @@
 \documentclass[
 	solutions,
 	singlenumbering
-]{../../../lib/tex/ormc_handout}
+]{../../../lib/tex/handout}
 \usepackage{../../../lib/tex/macros}
 
 \input{tikzset.tex}

src/Advanced/De Bruijn/tikzset.tex

@@ -24,7 +24,7 @@
 	label/.style = {
 		rectangle,
 		% For automatic red background in solutions
-		fill = \ORMCbgcolor,
+		fill = \bgcolor,
 		draw = none,
 		rounded corners = 0mm
 	},

src/Advanced/Definable Sets/main.tex

@@ -3,7 +3,7 @@
 \documentclass[
 	solutions,
 	singlenumbering
-]{../../../lib/tex/ormc_handout}
+]{../../../lib/tex/handout}
 \usepackage{../../../lib/tex/macros}
 
 

src/Advanced/Error-Correcting Codes/main.tex

@@ -3,7 +3,7 @@
 \documentclass[
 	solutions,
 	singlenumbering
-]{../../../lib/tex/ormc_handout}
+]{../../../lib/tex/handout}
 \usepackage{../../../lib/tex/macros}
 
 
@@ -16,6 +16,11 @@
 \title{Error-Correcting Codes}
 \subtitle{Prepared by Mark on \today}
 
+
+% TODO:
+% ISBN section is tedious, could use some work.
+% Check problem 5
+
 \begin{document}
 
 	\maketitle

src/Advanced/Error-Correcting Codes/parts/00 detection.tex

@@ -131,7 +131,7 @@ Take a valid ISBN-13 and swap two adjacent digits. When will the result be a val
 
 \vfill
 
-\problem{}<isbn-nocorrect>
+\problem{}<isbnnocorrect>
 \texttt{978-008-2066-466} was a valid ISBN until I changed a single digit. \par
 Can you find the digit I changed? Can you recover the original ISBN?
 

src/Advanced/Error-Correcting Codes/parts/01 correction.tex

@@ -1,6 +1,6 @@
 \section{Error Correction}
 
-As we saw in \ref{isbn-nocorrect}, the ISBN check-digit scheme does not allow us to correct errors. \par
+As we saw in \ref{isbnnocorrect}, the ISBN check-digit scheme does not allow us to correct errors. \par
 QR codes feature a system that does. \par
 
 \vspace{1mm}

src/Advanced/Esoteric Languages/main.tex

@@ -3,7 +3,7 @@
 \documentclass[
 	nosolutions,
 	singlenumbering
-]{../../../lib/tex/ormc_handout}
+]{../../../lib/tex/handout}
 \usepackage{../../../lib/tex/macros}
 
 

src/Advanced/Estimathon/main.tex

@@ -4,7 +4,7 @@
 	solutions,
 	singlenumbering,
 	nopagenumber
-]{../../../lib/tex/ormc_handout}
+]{../../../lib/tex/handout}
 \usepackage{../../../lib/tex/macros}
 
 \uptitlel{Advanced 2}

src/Advanced/Generating Functions/main.tex

@@ -3,7 +3,7 @@
 \documentclass[
 	solutions,
 	singlenumbering
-]{../../../lib/tex/ormc_handout}
+]{../../../lib/tex/handout}
 \usepackage{../../../lib/tex/macros}
 
 

src/Advanced/Geometric Optimization/main.tex

@@ -2,7 +2,7 @@
 % use [solutions] flag to show solutions.
 \documentclass[
 	solutions
-]{../../../lib/tex/ormc_handout}
+]{../../../lib/tex/handout}
 \usepackage{../../../lib/tex/macros}
 
 \uptitlel{Advanced 2}

src/Advanced/Geometry of Masses/main.tex

@@ -4,7 +4,7 @@
 	solutions,
 	singlenumbering,
 	shortwarning
-]{../../../lib/tex/ormc_handout}
+]{../../../lib/tex/handout}
 \usepackage{../../../lib/tex/macros}
 
 \usepackage{tikz}

src/Advanced/Graph Algorithms/main.tex

@@ -2,7 +2,7 @@
 % use [solutions] flag to show solutions.
 \documentclass[
 	solutions
-]{../../../lib/tex/ormc_handout}
+]{../../../lib/tex/handout}
 \usepackage{../../../lib/tex/macros}
 
 \input{tikxset}

src/Advanced/Graph Algorithms/tikxset.tex

@@ -22,7 +22,7 @@
 	label/.style = {
 		circle,
 		% For automatic red background in solutions
-		fill = \ORMCbgcolor,
+		fill = \bgcolor,
 		draw = none
 	},
 	%

src/Advanced/Intro to Proofs/main.tex

@@ -3,7 +3,7 @@
 \documentclass[
 	nosolutions,
 	singlenumbering
-]{../../../lib/tex/ormc_handout}
+]{../../../lib/tex/handout}
 \usepackage{../../../lib/tex/macros}
 
 

src/Advanced/Introduction to Quantum/main.tex

@@ -1,7 +1,7 @@
 \documentclass[
 	solutions,
 	singlenumbering
-]{../../../lib/tex/ormc_handout}
+]{../../../lib/tex/handout}
 \usepackage{../../../lib/tex/macros}
 \usepackage{units}
 \input{src/tikzset}

src/Advanced/Introduction to Quantum/src/main.tex

@@ -3,7 +3,7 @@
 \documentclass[
 	solutions,
 	singlenumbering
-]{../../../../lib/tex/ormc_handout}
+]{../../../../lib/tex/handout}
 \usepackage{../../../../lib/tex/macros}
 \usepackage{units}
 \input{tikzset}

src/Advanced/Introduction to Quantum/src/parts/01 bits.tex

@@ -462,7 +462,7 @@ Thus,
 \end{equation*}
 
 
-\begin{ORMCbox}{Review: Multiplying Vectors by Matrices}{black!10!white}{black!65!white}
+\begin{hobox}{Review: Multiplying Vectors by Matrices}{black!10!white}{black!65!white}
 	\begin{equation*}
 		Av =
 		\begin{bmatrix}
@@ -480,7 +480,7 @@ Thus,
 	\end{equation*}
 
 	Note that each element of $Av$ is the dot product of a row in $A$ and a column in $v$.
-\end{ORMCbox}
+\end{hobox}
 
 \problem{}
 Compute the following product:

src/Advanced/Introduction to Quantum/src/parts/05 quantum gates.tex

@@ -154,7 +154,7 @@ The \textit{Hadamard Gate} is given by the following matrix: \par
 \end{equation*}
 \note{Note that we divide by $\sqrt{2}$, since $H$ must be orthonormal.}
 
-\begin{ORMCbox}{Review: Matrix Multiplication}{black!10!white}{black!65!white}
+\begin{hobox}{Review: Matrix Multiplication}{black!10!white}{black!65!white}
 	Matrix multiplication works as follows:
 
 	\begin{equation*}
@@ -196,7 +196,7 @@ The \textit{Hadamard Gate} is given by the following matrix: \par
 
 	This is exactly the first column of the matrix product. \par
 	Also, note that each element of $Ac_0$ is the dot product of a row in $A$ and a column in $c_0$.
-\end{ORMCbox}
+\end{hobox}
 
 
 \problem{}

src/Advanced/Introduction to Quantum/src/tikzset.tex

@@ -13,7 +13,7 @@
 		line width = 0.35mm
 	},
 	qubit/.style = {
-		fill = \ORMCbgcolor,
+		fill = \bgcolor,
 		line width = 0.35mm
 	},
 	wire/.style = {

src/Advanced/Lambda Calculus/main.tex

@@ -3,7 +3,7 @@
 \documentclass[
 	solutions,
 	singlenumbering
-]{../../../lib/tex/ormc_handout}
+]{../../../lib/tex/handout}
 \usepackage{../../../lib/tex/macros}
 
 

src/Advanced/Lattices/main.tex

@@ -3,7 +3,7 @@
 \documentclass[
 	solutions,
 	singlenumbering
-]{../../../lib/tex/ormc_handout}
+]{../../../lib/tex/handout}
 \usepackage{../../../lib/tex/macros}
 
 \usepackage{ifthen}

src/Advanced/Lattices/parts/0 intro.tex

@@ -1,5 +1,6 @@
 \definition{}
-The \textit{integer lattice} $\mathbb{Z}^n \subset \mathbb{R}^n$ is the set of points with integer coordinates.
+The \textit{integer lattice} $\mathbb{Z}^n$ is the set of points with integer coordinates in $n$ dimensions. \par
+For example, $\mathbb{Z}^3$ is the set of points $(a, b, c)$ where $a$, $b$, and $c$ are integers.
 
 \problem{}
 Draw $\mathbb{Z}^2$.
@@ -8,12 +9,13 @@ Draw $\mathbb{Z}^2$.
 
 
 \definition{}
-We say a set of vectors $\{v_1, v_2, ..., v_k\}$ \textit{generates} $\mathbb{Z}^n$ if every lattice point can be written uniquely as
+We say a set of vectors $\{v_1, v_2, ..., v_k\}$ \textit{generates} $\mathbb{Z}^n$
+if every lattice point can be written as
 $$
 	a_1v_1 + a_2v_2 + ... + a_kv_k
 $$
 for integer coefficients $a_i$. \par
-It is fairly easy to show that $k$ must be at least $n$.
+\textbf{Bonus:} show that $k$ must be at least $n$.
 
 \problem{}
 Which of the following generate $\mathbb{Z}^2$?
@@ -30,8 +32,7 @@ Which of the following generate $\mathbb{Z}^2$?
 \vfill
 
 \problem{}
-Find a set of two vectors that generates $\mathbb{Z}^2$. \\
-Don't say $\{ (0, 1), (1, 0) \}$, that's too easy.
+Find a set of two vectors other than $\{ (0, 1), (1, 0) \}$ that generates $\mathbb{Z}^2$. \\
 
 \vfill
 
@@ -44,7 +45,8 @@ Find a set of vectors that generates $\mathbb{Z}^n$.
 \pagebreak
 
 \definition{}
-A \textit{fundamental region} of a lattice is the parallelepiped spanned by a generating set. The exact shape of this region depends on the generating set we use.
+Say we have a generating set of a lattice. \par
+The \textit{fundamental region} of this set is the $n$-dimensional parallelogram spanned by its members. \par
 
 \problem{}
 Draw two fundamental regions of $\mathbb{Z}^2$ using two different generating sets. Verify that their volumes are the same.

src/Advanced/Lattices/parts/1 minkowski.tex

@@ -1,6 +1,6 @@
 \section{Minkowski's Theorem}
 
-\theorem{Blichfeldt's Theorem}
+\theorem{Blichfeldt's Theorem}<blich>
 Let $X$ be a finite connected region. If the volume of $X$ is greater than $1$, $X$ must contain two distinct points that differ by an element of $\mathbb{Z}^n$. In other words, there exist distinct $x, y \in X$ so that $x - y \in \mathbb{Z}^n$.
 
 \vspace{2mm}
@@ -9,14 +9,22 @@ Intuitively, this means that you can translate $X$ to cover two lattice points a
 
 
 \problem{}
-Draw a region in $\mathbb{R}^2$ with volume greater than 1 that contains no lattice points. Find two points in that region which differ by an integer vector.
+Draw a connected region in $\mathbb{R}^2$ with volume greater than 1 that contains no lattice points. Find two points in that region which differ by an integer vector.
 \hint{Area is two-dimensional volume.}
 
 \vfill
 
 
 \problem{}
-The following picture gives an idea for the proof of Blichfeldt's theorem in $\mathbb{Z}^2$. Explain the picture and complete the proof.
+Draw a \textit{disconnected} region in $\mathbb{R}^2$ with volume greater than 1 that contains no lattice points, \par
+and show that no two points in that region differ by an integer vector.
+\note{In other words, show that \ref{blich} indeed requires a connected region.}
+
+\vfill
+
+\problem{}
+The following picture gives an idea for the proof of Blichfeldt's theorem in $\mathbb{Z}^2$. \par
+Explain the picture and complete the proof.
 
 \begin{center}
 	\includegraphics[angle=90,width=0.5\linewidth]{proof.png}
@@ -48,10 +56,8 @@ Let $X$ be a region $\in \mathbb{R}^2$ of volume $k$. How many integral points m
 A region $X$ is \textit{convex} if the line segment connecting any two points in $X$ lies entirely in $X$.
 
 \problem{}
-\begin{itemize}
-	\item Draw a convex region in the plane.
-	\item Draw a region that is not convex.
-\end{itemize}
+Draw a convex region in two dimensions. \par
+Then, draw a two-dimensional region that is \textit{not} convex.
 
 \vfill
 \pagebreak
@@ -59,23 +65,28 @@ A region $X$ is \textit{convex} if the line segment connecting any two points in
 
 
 \definition{}
-We say a region $X$ is \textit{symmetric} if for all points $x \in X$, $-x$ is also in $X$.
+We say a region $X$ is \textit{symmetric with respect to the origin} if for all points $x \in X$, $-x$ is also in $X$. \par
+In the following problems, \say{\textit{symmetric}} means \say{symmetric with respect to the origin.}
 
 \problem{}
-\begin{itemize}
-	\item Draw a symmetric region.
-	\item Draw an asymmetric region.
-\end{itemize}
+Draw a symmetric region. \par
+Then, draw an asymmetric region.
+
+\vfill
+
+\problem{}
+Show that a convex symmetric set always contains the origin.
 
 \vfill
 
 \theorem{Minkowski's Theorem}<mink>
-Every convex set in $\mathbb{R}^n$ that is symmetric with respect to the origin and which has a volume greater than $2^n$ contains an integral point that isn't zero.
+Every convex set in $\mathbb{R}^n$ that is symmetric and has a volume \par
+greater than $2^n$ contains an integral point that isn't zero.
 
 
 \problem{}
 Draw a few sets that satisfy \ref{mink} in $\mathbb{R}^2$. \par
-What is the simplest region that has the properties listed above?
+What is a simple class of regions that has the properties listed above?
 
 \vfill
 

src/Advanced/Mock a Mockingbird/main.tex

@@ -3,7 +3,7 @@
 \documentclass[
 	solutions,
 	singlenumbering
-]{../../../lib/tex/ormc_handout}
+]{../../../lib/tex/handout}
 \usepackage{../../../lib/tex/macros}
 
 

src/Advanced/Nonstandard Analysis/main.tex

@@ -3,7 +3,7 @@
 \documentclass[
 	nosolutions,
 	singlenumbering,
-]{../../../lib/tex/ormc_handout}
+]{../../../lib/tex/handout}
 \usepackage{../../../lib/tex/macros}
 \usepackage{units}
 

src/Advanced/Origami/main.tex

@@ -3,7 +3,7 @@
 \documentclass[
 	solutions,
 	%shortwarning
-]{../../../lib/tex/ormc_handout}
+]{../../../lib/tex/handout}
 \usepackage{../../../lib/tex/macros}
 
 \graphicspath{ {./images/} }

src/Advanced/Pidgeonhole Problems/main.tex

@@ -2,7 +2,7 @@
 % use [solutions] flag to show solutions.
 \documentclass[
 	solutions
-]{../../../lib/tex/ormc_handout}
+]{../../../lib/tex/handout}
 \usepackage{../../../lib/tex/macros}
 
 \usepackage{amsmath}

src/Advanced/Random Walks/main.tex

@@ -3,7 +3,7 @@
 \documentclass[
 	solutions,
 	singlenumbering
-]{../../../lib/tex/ormc_handout}
+]{../../../lib/tex/handout}
 \usepackage{../../../lib/tex/macros}
 
 \input{tikxset.tex}

src/Advanced/Random Walks/tikxset.tex

@@ -24,7 +24,7 @@
 	label/.style = {
 		rectangle,
 		% For automatic red background in solutions
-		fill = \ORMCbgcolor,
+		fill = \bgcolor,
 		draw = none,
 		rounded corners = 0mm
 	},

src/Advanced/Relativity/main.tex

@@ -4,7 +4,7 @@
 	solutions,
 	singlenumbering,
 	shortwarning
-]{../../../lib/tex/ormc_handout}
+]{../../../lib/tex/handout}
 \usepackage{../../../lib/tex/macros}
 \input{diagram}
 

src/Advanced/Retrograde Analysis/main.tex

@@ -3,7 +3,7 @@
 \documentclass[
 	solutions,
 	shortwarning
-]{../../../lib/tex/ormc_handout}
+]{../../../lib/tex/handout}
 \usepackage{../../../lib/tex/macros}
 
 \usepackage{chessfss}

src/Advanced/Size of Sets/main.tex

@@ -3,7 +3,7 @@
 \documentclass[
 	solutions,
 	singlenumbering
-]{../../../lib/tex/ormc_handout}
+]{../../../lib/tex/handout}
 \usepackage{../../../lib/tex/macros}
 
 

src/Advanced/Stopping Problems/main.tex

@@ -3,7 +3,7 @@
 \documentclass[
 	solutions,
 	singlenumbering
-]{../../../lib/tex/ormc_handout}
+]{../../../lib/tex/handout}
 \usepackage{../../../lib/tex/macros}
 
 \usepackage{units}

src/Advanced/Symmetric Groups/main.tex

@@ -3,7 +3,7 @@
 \documentclass[
 	solutions,
 	singlenumbering
-]{../../../lib/tex/ormc_handout}
+]{../../../lib/tex/handout}
 \usepackage{../../../lib/tex/macros}
 \usetikzlibrary{calc}
 

src/Advanced/Wallpaper/main.typ

@@ -0,0 +1,26 @@
+#import "@local/handout:0.1.0": *
+
+// Resources:
+//
+// https://eschermath.org/wiki/Wallpaper_Patterns.html
+// https://mathworld.wolfram.com/WallpaperGroups.html
+// https://en.wikipedia.org/wiki/Wallpaper_group
+
+#show: handout.with(
+  title: [Wallpaper Symmetry],
+  by: "Mark",
+)
+
+#include "parts/00 intro.typ"
+#pagebreak()
+
+#include "parts/01 reflect.typ"
+#pagebreak()
+
+#include "parts/02 rotate.typ"
+#pagebreak()
+
+#include "parts/03 problems.typ"
+#pagebreak()
+
+#include "parts/04 theorem.typ"

src/Advanced/Wallpaper/meta.toml

@@ -0,0 +1,7 @@
+[metadata]
+title = "Wallpaper Symmetries"
+
+
+[publish]
+handout = true
+solutions = true

src/Advanced/Wallpaper/parts/00 intro.typ

@@ -0,0 +1,151 @@
+#import "@local/handout:0.1.0": *
+#import "@preview/cetz:0.3.1"
+
+= Wallpaper Symmetries
+
+#definition()
+A _Euclidean isometry_ is a transformation of the plane that preserves distances. \
+Intuitively, an isometry moves objects on the plane without deforming them.
+
+There are four classes of Euclidean isometries:
+- translations
+- reflections
+- rotations
+- glide reflections
+#note([We can prove there are no others, but this is beyond the scope of this handout.]) \
+A simple example of each isometry is shown below:
+
+#let demo(c) = {
+  let s = 0.5
+  cetz.draw.line(
+    (0, 0),
+    (3 * s, 0),
+    (3 * s, 1 * s),
+    (1 * s, 1 * s),
+    (1 * s, 2 * s),
+    (0, 2 * s),
+    close: true,
+    fill: c,
+    stroke: black + 0mm * s,
+  )
+}
+
+#table(
+  stroke: none,
+  align: center,
+  columns: (1fr, 1fr),
+  rows: (3.5cm, 3.5cm),
+  row-gutter: 2mm,
+  [
+    #cetz.canvas({
+      import cetz.draw: *
+
+      demo(ored)
+      translate(x: -1.0, y: -1.0)
+      demo(oblue)
+    })
+    #v(1fr)
+    Translation
+  ],
+  [
+    #cetz.canvas({
+      import cetz.draw: *
+
+      circle((-2, 0), radius: 0.1, stroke: none, fill: black)
+      arc(
+        (-2, 0),
+        radius: 1,
+        anchor: "origin",
+        start: 0deg,
+        stop: -30deg,
+        mode: "PIE",
+      )
+
+      demo(ored)
+      rotate(z: -30deg, origin: (-2, 0))
+      demo(oblue)
+    })
+    #v(1fr)
+    Rotation
+  ],
+
+  [
+    #cetz.canvas({
+      import cetz.draw: *
+
+      line((-2, 0), (4, 0))
+
+      translate(x: 0, y: 0.25)
+      demo(ored)
+      set-transform(none)
+
+      set-transform((
+        (1, 0, 0, 0),
+        (0, 1, 0, 0),
+        (0, 0, 1, 0),
+        (0, 0, 0, 1),
+      ))
+
+      translate(x: 0, y: 0.25)
+      demo(oblue)
+    })
+    #v(1fr)
+    Reflection
+  ],
+  [
+    #cetz.canvas({
+      import cetz.draw: *
+
+
+      demo(ored)
+
+      set-transform((
+        (1, 0, 0, 0),
+        (0, 1, 0, 0),
+        (0, 0, 0, 0),
+        (0, 0, 0, 0),
+      ))
+      translate(x: 2, y: 0)
+
+      demo(oblue)
+
+      set-transform(none)
+      line((-1, 0), (5, 0))
+    })
+    #v(1fr)
+    Glide reflection
+  ],
+)
+
+#definition()
+A _wallpaper_ is a two-dimensional pattern that...
+- has translational symmetry in at least two non-parallel directions (and therefore fills the plane) \
+  #note[
+    "Translational symmetry" means that we can slide the entire wallpaper in some direction, \
+    eventually mapping the pattern to itself.]
+- has a countable number of reflection, rotation, or glide symmetries. \
+
+#v(1fr)
+#pagebreak()
+
+#problem()
+Is a plain square grid a valid wallpaper?
+
+#solution([
+  Yes!
+  - It has translational symmetry in the horizontal and vertical directions
+  - It has a countable number of symmetries---namely, six distinct mirror lines (horizontal, vertical, and diagonal) duplicated once per square.
+  - A square grid is #sym.convolve`442`
+])
+
+#v(1fr)
+
+
+#problem()
+Is the empty plane a valid wallpaper?
+
+#solution([
+  No, since it has uncountably many symmetries.
+])
+
+#v(1fr)

src/Advanced/Wallpaper/parts/01 reflect.typ

@@ -0,0 +1,132 @@
+#import "@local/handout:0.1.0": *
+#import "@preview/cetz:0.3.1"
+
+= Mirror Symmetry
+
+#definition()
+A _reflection_ is a transformation of the plane obtained by reflecting all points about a line. \
+If this reflection maps the wallpaper to itself, we have a _mirror symmetry_. \
+
+If $n$ such mirror lines intersect at a point, they form a _mirror node of order $n$_. \
+#note[Mirror nodes with order 1 do not exist (i.e, $n >= 2$). A line does not intersect itself!]
+
+#v(2mm)
+
+Two mirror nodes on a wallpaper are identical if we can map one to the other with a translation and a rotation while preserving the pattern on that wallpaper.
+
+#problem(label: "pat333")
+Find all three distinct mirror nodes in the following pattern. \
+What is the order of each node? \
+#hint([
+  You may notice rotational symmetry in this pattern. \
+  Don't worry about that yet, we'll discuss it later.
+])
+
+#table(
+  stroke: none,
+  align: center,
+  columns: 1fr,
+  rows: 45mm,
+  image("../res/wolfram/p3m1.svg", height: 100%),
+)
+
+#solution([
+  The mirror nodes are:
+  - the center of the amber cross
+  - the center of each right-handed group of three adjacent hexagons
+  - the center of each left-handed group of three adjacent hexagons
+])
+
+#v(1fr)
+
+
+#definition()
+_Orbifold notation_ gives us a way to describe the symmetries of a wallpaper. \
+It defines a _signature_ that fully describes all the symmetries of a given pattern. \
+We will introduce orbifold notation one symmetry at a time.
+
+#definition()
+In orbifold notation, mirror nodes are denoted by a #sym.convolve followed by a list of integer. \
+Every integer $n$ following a #sym.convolve denotes a mirror node of order $n$.
+
+#v(2mm)
+
+The order of these integers doesn't matter. #sym.convolve`234` and #sym.convolve`423` are the same signature. \
+However, we usually denote $n$-fold symmetries in descending order (that is, like #sym.convolve`432`). \
+If we have many nodes of the same order, integers may be repeated.
+
+
+#problem()
+What is the signature of the wallpaper in @pat333? \
+#hint[Again, ignore rotational symmetry for now.]
+#solution([It is #sym.convolve`333`])
+
+
+// MARK: page
+#v(1fr)
+#pagebreak()
+
+#problem()
+Find the signature of the following pattern.
+
+#table(
+  stroke: none,
+  align: center,
+  columns: 1fr,
+  rows: 60mm,
+  image("../res/*632-a.png", height: 100%),
+)
+
+
+#solution([
+  It is #sym.convolve`632`:
+  #table(
+    stroke: none,
+    align: center,
+    columns: 1fr,
+    rows: 40mm,
+    image("../res/*632-b.png", height: 100%),
+  )
+])
+
+#v(1fr)
+
+#problem()
+Draw a wallpaper pattern with signature #sym.convolve`2222`
+
+#solution([
+  Sample solutions are below.
+
+  #table(
+    stroke: none,
+    align: center,
+    columns: (1fr, 1fr),
+    rows: 50mm,
+    image("../res/wolfram/pmm.svg", height: 100%),
+    image("../res/escher/pmm.svg", height: 100%),
+  )
+])
+
+#v(1fr)
+
+#pagebreak()
+
+
+#remark()
+In an exceptional case, we have two parallel mirror lines. \
+Consider the following pattern:
+
+#table(
+  stroke: none,
+  align: center,
+  columns: 1fr,
+  rows: 60mm,
+  image("../res/**.png", height: 100%),
+)
+
+The signature of this pattern is #sym.convolve#sym.convolve
+
+#problem()
+Draw another wallpaper pattern with signature #sym.convolve#sym.convolve.
+
+#v(1fr)

src/Advanced/Wallpaper/parts/02 rotate.typ

@@ -0,0 +1,181 @@
+#import "@local/handout:0.1.0": *
+#import "@preview/cetz:0.3.1"
+
+= Rotational Symmetry
+
+
+#definition()
+A wallpaper may also have $n$-fold rotational symmetry about a point.
+#v(2mm)
+This means there are no more than $n$ rotations around that point that map the wallpaper to itself.
+#v(2mm)
+As before, two points of rotational symmetry are identical if we can perform a translation and rotation that maps one to the other without changing the wallpaper.
+
+#definition()
+In orbifold notation, rotation is specified similarly to reflection, but uses the prefix #sym.diamond.stroked.small. \
+For example:
+- #sym.diamond.stroked.small`333` denotes a pattern with three distinct centers of rotation of order 3.
+- #sym.diamond.stroked.small`4`#sym.convolve`2` denotes a pattern with one rotation center of order 4 and one mirror node of order 2.
+
+#table(
+  stroke: none,
+  align: center,
+  columns: (1fr, 1fr),
+  rows: 50mm,
+  image("../res/333.png", height: 100%), image("../res/3*3.png", height: 100%),
+)
+
+
+#problem()
+Find the three rotation centers in the left wallpaper. \
+What are their orders?
+
+#solution([This is #sym.diamond.stroked.small`333`])
+
+#v(1fr)
+
+#problem()
+Find the signature of the pattern on the right.
+
+#solution([This is #sym.diamond.stroked.small`3`#sym.convolve`3`])
+
+#v(1fr)
+
+
+#remark()
+You may have noticed that we could have an ambiguous classification, since two reflections are equivalent to a translation and a rotation.
+We thus make the following distinction: _rotational symmetry that can be explained by reflection is not rotational symmetry._
+
+#v(2mm)
+
+In other words, when classifying a pattern...
+- we first find all mirror symmetries,
+- then all rotational symmetries that are not accounted for by reflection.
+
+#pagebreak()
+
+
+// MARK: glide
+
+= Glide Reflections
+
+#definition()
+Another type of symmetry is the _glide reflection_, denoted #sym.times.
+
+A glide reflection is the result of a translation along a line followed by reflection about that line.
+
+For example, consider the following pattern:
+#table(
+  stroke: none,
+  align: center,
+  columns: 1fr,
+  rows: 60mm,
+  image("../res/*x-a.png", height: 100%),
+)
+
+#problem()
+Convince yourself that all mirror lines in this pattern are _not_ distinct. /
+In other words, this pattern has only one mirror symmetry.
+
+#solution([
+  There may seem to be two, but they are identical. \
+  We can translate one onto the other.
+])
+
+#v(1fr)
+
+
+
+#problem()
+Use the following picture to find the glide reflection in the above pattern.
+#table(
+  stroke: none,
+  align: center,
+  columns: 1fr,
+  rows: 70mm,
+  image("../res/*x-b.png", height: 100%),
+)
+
+#v(1fr)
+
+#remark()
+The signature of this wallpaper is #sym.convolve#sym.times.
+
+#pagebreak()
+
+
+#definition()
+If none of the above symmetries appear in a pattern, then we only have simple translational symmetry. We denote this with the signature #sym.circle.small.
+
+#remark()
+In summary, to find the signature of a pattern:
+- find the mirror lines (#sym.convolve) and the distinct intersections;
+- then find the rotation centers (#sym.diamond.stroked.small) not explained by reflection;
+- then find all glide reflections (#sym.times) that do not cross a mirror line.
+- If we have none of the above, our pattern must be #sym.circle.small.
+
+
+
+#problem()
+Find the signature of the following pattern:
+
+#table(
+  stroke: none,
+  align: center,
+  columns: 1fr,
+  rows: 50mm,
+  image("../res/wiki/Wallpaper_group-cm-4.jpg", height: 100%),
+)
+
+#solution([
+  This is #sym.convolve#sym.times.
+])
+
+#v(1fr)
+
+
+#problem()
+Find the signature of the following pattern:
+
+#table(
+  stroke: none,
+  align: center,
+  columns: 1fr,
+  rows: 60mm,
+  image("../res/wiki/Wallpaper_group-p4g-2.jpg", height: 100%),
+)
+
+#solution([
+  This is #sym.diamond.stroked.small`4`#sym.convolve`2`
+])
+
+#v(1fr)
+
+
+
+#pagebreak()
+
+#problem()
+Find two glide reflections in the following pattern.\
+#note[(and thus show that its signature is #sym.times#sym.times.)]
+
+
+#table(
+  stroke: none,
+  align: center,
+  columns: 1fr,
+  rows: 70mm,
+  image("../res/xx-b.png", height: 100%),
+)
+
+#solution([
+  #table(
+    stroke: none,
+    align: center,
+    columns: 1fr,
+    rows: 40mm,
+    image("../res/xx-a.png", height: 100%),
+  )
+])
+
+#v(1fr)

src/Advanced/Wallpaper/parts/03 problems.typ

@@ -0,0 +1,67 @@
+#import "@local/handout:0.1.0": *
+#import "@preview/cetz:0.3.1"
+
+#let pat(img, sol) = {
+  problem()
+
+  table(
+    stroke: none,
+    align: center,
+    columns: (1fr, 1fr),
+    rows: 80mm,
+    image(img, height: 100%), image(img, height: 100%),
+  )
+
+  solution(sol)
+  v(1fr)
+}
+
+= A few problems
+
+Find the signatures of the following patterns. Mark all mirror nodes, rotation centers, and glide reflections. \
+Each pattern is provided twice for convenience.
+
+
+#pat("../res/wolfram/cm.svg", [#sym.times#sym.convolve])
+#pat("../res/wolfram/cmm.svg", [#sym.diamond.stroked`2`#sym.convolve`22`])
+#pagebreak()
+
+
+
+
+#pat("../res/wolfram/p3.svg", [#sym.diamond.stroked`333`])
+#pat("../res/wolfram/p3m1.svg", [#sym.convolve`333`])
+#pagebreak()
+
+#pat("../res/wolfram/p4.svg", [#sym.diamond.stroked`442`])
+#pat("../res/wolfram/p4m.svg", [#sym.convolve`442`])
+#pagebreak()
+
+#pat("../res/wolfram/p6.svg", [#sym.diamond.stroked`632`])
+#pat("../res/wolfram/p6m.svg", [#sym.convolve`632`])
+#pagebreak()
+
+#pat("../res/wolfram/p4g.svg", [#sym.diamond.stroked`4`#sym.convolve`2`])
+#pat("../res/wolfram/p31m.svg", [#sym.diamond.stroked`3`#sym.convolve`3`])
+#pagebreak()
+
+#problem()
+Draw a wallpaper with the signature #sym.convolve`442` \
+#note[Make sure there are no other symmetries!]
+#v(1fr)
+#pagebreak()
+
+
+#pat("../res/wolfram/pgg.svg", [#sym.diamond.stroked`22`#sym.times])
+#pat("../res/wolfram/pmg.svg", [#sym.diamond.stroked`22`#sym.convolve])
+#pagebreak()
+
+#pat("../res/wolfram/pg.svg", [#sym.times#sym.times])
+#pat("../res/wolfram/pm.svg", [#sym.convolve#sym.convolve])
+#pagebreak()
+
+#pat("../res/wolfram/p2.svg", [#sym.diamond.stroked`2222`])
+#pat("../res/wolfram/pmm.svg", [#sym.convolve`2222`])
+#pagebreak()
+
+#pat("../res/wolfram/p1.svg", [#sym.circle.small])

src/Advanced/Wallpaper/parts/04 theorem.typ

@@ -0,0 +1,100 @@
+#import "@local/handout:0.1.0": *
+#import "@preview/cetz:0.3.1"
+
+= The Signature-Cost Theorem
+
+#definition()
+First, we'll associate a _cost_ to each type of symmetry in orbifold notation:
+
+#v(4mm)
+#align(
+  center,
+  table(
+    stroke: (1pt, 1pt),
+    align: center,
+    columns: (auto, auto, auto, auto),
+    [*Symbol*], [*Cost*], [*Symbol*], [*Cost*],
+    [#sym.circle.small], [2], [#sym.times or #sym.convolve], [1],
+    [#sym.diamond.stroked.small`2`], [1/2], [#sym.convolve`2`], [1/4],
+    [#sym.diamond.stroked.small`3`], [2/3], [#sym.convolve`3`], [1/3],
+    [#sym.dots], [#sym.dots], [#sym.dots], [#sym.dots],
+    [#sym.diamond.stroked.small`n`],
+    [$(n-1) / n$],
+    [#sym.convolve`n`],
+    [$(n-1) / (2n)$],
+  ),
+)
+
+
+We then calculate the total "cost" of a signature by adding up the costs of each component.
+
+For example, a pattern with signature #sym.convolve`333` has cost 2:
+
+#v(2mm)
+
+$
+  2 / 3 + 2 / 3 + 2 / 3 = 2
+$
+
+#problem()
+Calculate the costs of the following signatures:
+- #sym.diamond.stroked.small`3`#sym.convolve`3`
+- #sym.convolve#sym.convolve
+- #sym.diamond.stroked.small`4`#sym.convolve`2`:
+
+#solution([
+  - #sym.diamond.stroked.small`3`#sym.convolve`3`: $2/3 + 1 + 1/3 = 2$
+  - #sym.convolve#sym.convolve: $1 + 1 = 2$
+  - #sym.diamond.stroked.small`4`#sym.convolve`2`: $3/4 + 1 + 1/4 = 2$
+])
+
+#v(1fr)
+
+#theorem(name: "Signature Cost Theorem")
+The signatures of planar wallpaper patterns are exactly those with total cost 2. \
+#note([We will not prove this theorem today, accept it without proof.])
+
+#problem()
+Consider the 4 symmetries (translation, reflection, rotation, and glide reflection). \
+Which preserve orientation? Which reverse orientation?
+
+#solution([
+  - Reflections and glide reflections reverse orientation (directions of spirals).
+  - Translation and rotation preserve orientation.
+])
+
+#v(1fr)
+#pagebreak()
+
+#problem()
+Use the signature-cost theorem to find all the signatures consisting of only #sym.circle.small or rotational symmetries.
+
+#solution([
+  #sym.diamond.stroked.small`632`, #sym.diamond.stroked.small`442`, #sym.diamond.stroked.small`333`, #sym.diamond.stroked.small`2222`, #sym.circle.small
+])
+
+#v(1fr)
+
+
+#problem()
+Find all the signatures consisting of only mirror symmetries.
+
+#solution([
+  #sym.convolve`632`, #sym.convolve`442`, #sym.convolve`333`, #sym.convolve`2222`, #sym.convolve#sym.convolve
+])
+
+#v(1fr)
+
+
+#problem()
+Find all the remaining signatures. \
+Each must be a mix of of mirror symmetries, rotational symmetries, or glide reflections. \
+#hint([They are all shown in the problems section.])
+
+#solution([
+  #sym.diamond.stroked.small`3`#sym.convolve`3`, #sym.diamond.stroked.small`4`#sym.convolve`2`,
+  #sym.diamond.stroked.small`22`#sym.times, #sym.diamond.stroked.small`22`#sym.convolve,
+  #sym.times#sym.times, #sym.times#sym.convolve
+])
+
+#v(1fr)

src/Advanced/Wallpaper/res/escher/pmm.svg

@@ -0,0 +1,86 @@
+<?xml version="1.0" standalone="no"?>
+<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 20001102//EN" "http://www.w3.org/TR/2000/CR-SVG-20001102/DTD/svg-20001102.dtd">
+<svg xmlns:svg="http://www.w3.org/2000/svg" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" width="10.16cm" height="5.08cm" viewBox="0 0 384 192">
+<title>pmm</title>
+<desc>Exported by Tess 1.70.</desc>
+<clipPath id="mainclip"><rect x="0" y="0" width="384" height="192"/></clipPath>
+<g style="fill-rule:evenodd; stroke-linejoin:round; stroke-linecap:round; clip-path:url(#mainclip)">
+<defs>
+<g id="Tess0p">
+<path d="
+M7.1306642022,-41.0013191628 
+L7.1306642022,-7.1306642022 
+L89.1333025278,-7.1306642022 
+L7.1306642022,-42.7839852134 
+"/></g>
+<g id="Tess0" style="fill:none; stroke:none"><use xlink:href="#Tess0p"/></g>
+<g id="Tess1" style="fill:none; stroke:rgb(0,0,0); stroke-width:1.7826660506"><use xlink:href="#Tess0p"/></g>
+</defs>
+<g transform="translate(192,96) rotate(0) scale(0.5609575611,0.5609575611)">
+<g transform="translate(-405.2631578947,-100)"><use xlink:href="#Tess1"/></g>
+<g transform="translate(-405.2631578947,0)"><use xlink:href="#Tess1"/></g>
+<g transform="translate(-405.2631578947,100)"><use xlink:href="#Tess1"/></g>
+<g transform="translate(-405.2631578947,200)"><use xlink:href="#Tess1"/></g>
+<g transform="translate(-202.6315789474,-100)"><use xlink:href="#Tess1"/></g>
+<g transform="translate(-202.6315789474,0)"><use xlink:href="#Tess1"/></g>
+<g transform="translate(-202.6315789474,100)"><use xlink:href="#Tess1"/></g>
+<g transform="translate(-202.6315789474,200)"><use xlink:href="#Tess1"/></g>
+<g transform="translate(0,-100)"><use xlink:href="#Tess1"/></g>
+<g><use xlink:href="#Tess1"/></g>
+<g transform="translate(0,100)"><use xlink:href="#Tess1"/></g>
+<g transform="translate(0,200)"><use xlink:href="#Tess1"/></g>
+<g transform="translate(202.6315789474,-100)"><use xlink:href="#Tess1"/></g>
+<g transform="translate(202.6315789474,0)"><use xlink:href="#Tess1"/></g>
+<g transform="translate(202.6315789474,100)"><use xlink:href="#Tess1"/></g>
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+<g transform="translate(-202.6315789474,-200) rotate(180)"><use xlink:href="#Tess1"/></g>
+<g transform="translate(-202.6315789474,-100) rotate(180)"><use xlink:href="#Tess1"/></g>
+<g transform="translate(-202.6315789474,0) rotate(180)"><use xlink:href="#Tess1"/></g>
+<g transform="translate(-202.6315789474,100) rotate(180)"><use xlink:href="#Tess1"/></g>
+<g transform="translate(0,-200) rotate(180)"><use xlink:href="#Tess1"/></g>
+<g transform="translate(0,-100) rotate(180)"><use xlink:href="#Tess1"/></g>
+<g transform="rotate(180)"><use xlink:href="#Tess1"/></g>
+<g transform="translate(0,100) rotate(180)"><use xlink:href="#Tess1"/></g>
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+<g transform="rotate(180) scale(1,-1)"><use xlink:href="#Tess1"/></g>
+<g transform="translate(0,100) rotate(180) scale(1,-1)"><use xlink:href="#Tess1"/></g>
+<g transform="translate(0,200) rotate(180) scale(1,-1)"><use xlink:href="#Tess1"/></g>
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+<g transform="translate(202.6315789474,100) scale(1,-1)"><use xlink:href="#Tess1"/></g>
+</g>
+</g>
+</svg>

src/Intermediate/An Introduction to Graph Theory/main.tex

@@ -3,7 +3,7 @@
 \documentclass[
 	solutions,
 	singlenumbering
-]{../../../lib/tex/ormc_handout}
+]{../../../lib/tex/handout}
 \usepackage{../../../lib/tex/macros}
 
 

src/Intermediate/An Introduction to Graph Theory/tikxset.tex

@@ -24,7 +24,7 @@
 	label/.style = {
 		rectangle,
 		% For automatic red background in solutions
-		fill = \ORMCbgcolor,
+		fill = \bgcolor,
 		draw = none,
 		rounded corners = 0mm
 	},

src/Intermediate/Combinatorics/main.tex

@@ -2,7 +2,7 @@
 % use [solutions] flag to show solutions.
 \documentclass[
 	solutions
-]{../../../lib/tex/ormc_handout}
+]{../../../lib/tex/handout}
 \usepackage{../../../lib/tex/macros}
 
 

src/Intermediate/Instant Insanity/main.tex

@@ -2,7 +2,7 @@
 % use [solutions] flag to show solutions.
 \documentclass[
 	solutions
-]{../../../lib/tex/ormc_handout}
+]{../../../lib/tex/handout}
 \usepackage{../../../lib/tex/macros}
 
 

src/Intermediate/Newton's Laws/main.tex

@@ -2,7 +2,7 @@
 % use [solutions] flag to show solutions.
 \documentclass[
 	solutions
-]{../../../lib/tex/ormc_handout}
+]{../../../lib/tex/handout}
 \usepackage{../../../lib/tex/macros}
 
 

src/Intermediate/Probability/main.tex

@@ -1,6 +1,6 @@
 % use [nosolutions] flag to hide solutions.
 % use [solutions] flag to show solutions.
-\documentclass[solutions]{../../../lib/tex/ormc_handout}
+\documentclass[solutions]{../../../lib/tex/handout}
 \usepackage{../../../lib/tex/macros}
 
 

src/Intermediate/Proof Techniques/main.tex

@@ -3,7 +3,7 @@
 \documentclass[
 	solutions,
 	singlenumbering
-]{../../../lib/tex/ormc_handout}
+]{../../../lib/tex/handout}
 \usepackage{../../../lib/tex/macros}
 
 \usepackage{units}

src/Intermediate/Proof Techniques/parts/2 induction.tex

@@ -190,7 +190,7 @@ For example, see the proof of the statement in \ref{binomsum} on the next page.
 \pagebreak
 
 
-\begin{ORMCbox}{Alternative Proof}{ogrape!10!white}{ogrape}
+\begin{hobox}{Alternative Proof}{ogrape!10!white}{ogrape}
 	Consider the following problem: \par
 	How many ways are there to write a number $x$ as an ordered sum of positive integers? \par
 	\note{
@@ -234,7 +234,7 @@ For example, see the proof of the statement in \ref{binomsum} on the next page.
 	We've found that the number of ways to split $x$ can be written as either
 	$\sum_{n = 1}^{x-1} \binom{x-1}{n}$ or $2^{x-1}$,
 	and therefore $\sum_{n = 1}^{x-1} \binom{x-1}{n} = 2^{x-1}$.
-\end{ORMCbox}
+\end{hobox}
 
 
 \pagebreak

src/Intermediate/Slide Rules/main.tex

@@ -2,7 +2,7 @@
 % use [solutions] flag to show solutions.
 \documentclass[
 	solutions
-]{../../../lib/tex/ormc_handout}
+]{../../../lib/tex/handout}
 \usepackage{../../../lib/tex/macros}
 
 

src/Intermediate/Vectors 1/main.tex

@@ -1,6 +1,6 @@
 % use [nosolutions] flag to hide solutions.
 % use [solutions] flag to show solutions.
-\documentclass[solutions]{../../../lib/tex/ormc_handout}
+\documentclass[solutions]{../../../lib/tex/handout}
 \usepackage{adjustbox}
 \usepackage{../../../lib/tex/macros}
 

src/Intermediate/Vectors 2/main.tex

@@ -1,6 +1,6 @@
 % use [nosolutions] flag to hide solutions.
 % use [solutions] flag to show solutions.
-\documentclass[solutions]{../../../lib/tex/ormc_handout}
+\documentclass[solutions]{../../../lib/tex/handout}
 \usepackage{../../../lib/tex/macros}
 
 

src/Warm-Ups/Flip-Flops/main.tex

@@ -3,7 +3,7 @@
 	shortwarning,
 	singlenumbering,
 	nopagenumber
-]{../../../lib/tex/ormc_handout}
+]{../../../lib/tex/handout}
 \usepackage{../../../lib/tex/macros}
 \geometry{top = 20mm}
 

src/Warm-Ups/Ivan the Electrician/main.tex

@@ -3,7 +3,7 @@
 	hidewarning,
 	singlenumbering,
 	nopagenumber
-]{../../../lib/tex/ormc_handout}
+]{../../../lib/tex/handout}
 \usepackage{../../../lib/tex/macros}
 
 

src/Warm-Ups/Jump Chess/main.tex

@@ -3,7 +3,7 @@
 	hidewarning,
 	singlenumbering,
 	nopagenumber
-]{../../../lib/tex/ormc_handout}
+]{../../../lib/tex/handout}
 \usepackage{../../../lib/tex/macros}
 
 

src/Warm-Ups/Rootbound/main.tex

@@ -3,7 +3,7 @@
 	hidewarning,
 	singlenumbering,
 	nopagenumber
-]{../../../lib/tex/ormc_handout}
+]{../../../lib/tex/handout}
 \usepackage{../../../lib/tex/macros}
 
 \def\utri#1#2{
@@ -102,7 +102,7 @@
 
 	\vfill
 
-	\begin{ORMCbox}{Notes}{ogrape!10!white}{ogrape}
+	\begin{hobox}{Notes}{ogrape!10!white}{ogrape}
 		\begin{itemize}
 			\item
 			Each player needs to make multiple groups before the first player's second turn. \par
@@ -111,7 +111,7 @@
 
 			\item Groups are easiest to secure near the corners or along the edges. Play there first. \par
 		\end{itemize}
-	\end{ORMCbox}
+	\end{hobox}
 
 
 

src/Warm-Ups/Slide Rules/main.tex

@@ -3,7 +3,7 @@
 \documentclass[
 	solutions,
 	shortwarning
-]{../../../lib/tex/ormc_handout}
+]{../../../lib/tex/handout}
 \usepackage{../../../lib/tex/macros}